Problem: Solve for $x$ and $y$ using elimination. ${-2x+2y = 12}$ ${2x+3y = 23}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-2x$ and $2x$ cancel out. $5y = 35$ $\dfrac{5y}{{5}} = \dfrac{35}{{5}}$ ${y = 7}$ Now that you know ${y = 7}$ , plug it back into $\thinspace {-2x+2y = 12}\thinspace$ to find $x$ ${-2x + 2}{(7)}{= 12}$ $-2x+14 = 12$ $-2x+14{-14} = 12{-14}$ $-2x = -2$ $\dfrac{-2x}{{-2}} = \dfrac{-2}{{-2}}$ ${x = 1}$ You can also plug ${y = 7}$ into $\thinspace {2x+3y = 23}\thinspace$ and get the same answer for $x$ : ${2x + 3}{(7)}{= 23}$ ${x = 1}$